$A$ particle of mass $10 \,g$ is undergoing $S.H.M.$ with an amplitude of $10 \,cm$ and a period of $0.1 \,s$. The maximum value of the force on the particle is about ............ $N$.

The oscillation of a body on a smooth horizontal surface is represented by the equation $x = A \cos \omega t$,where $x$ is the displacement at time $t$ and $\omega$ is the angular frequency of oscillation. Which one of the following graphs correctly shows the variation of acceleration $a$ with time $t$?

The maximum acceleration of a particle in $SHM$ is made two times keeping the maximum speed constant. This is possible when:

This is the position-time graph of a mass on a spring. What can you say about the velocity and force at the instant indicated by the dashed line? (Positive direction is to the right.)

The acceleration of a particle performing $S.H.M.$ at a distance of $3\;cm$ from the mean position is $12\;cm/s^2$. Its time period is ..... $s$.

Which one of the following statements is true for the speed $v$ and the acceleration $a$ of a particle executing simple harmonic motion?